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%I #10 Nov 25 2019 01:04:32
%S 1,4,2,6,0,3,12,8,0,4,10,0,0,0,5,24,12,12,0,0,6,14,0,0,0,0,0,7,32,24,
%T 0,16,0,0,0,8,27,0,18,0,0,0,0,0,9,40,20,0,0,20,0,0,0,0,10,22,0,0,0,0,
%U 0,0,0,0,0,11,72,48,36,24,0,24,0,0,0,0,0,12,26,0,0,0,0,0,0,0,0,0,0,0,13,56,28,0,0
%N Triangle read by rows: T(n,k) is the sum of the parts congruent to 0 mod k in the partitions of n into equal parts, 1 <= k <= n.
%C Column k lists the terms of A038040 multiplied by k and interspersed with (k-1) zeros.
%F T(n,k) = A126988(n,k)*A134577(n,k).
%e Triangle begins:
%e 1;
%e 4, 2;
%e 6, 0, 3;
%e 12, 8, 0, 4;
%e 10, 0, 0, 0, 5;
%e 24, 12, 12, 0, 0, 6;
%e 14, 0, 0, 0, 0, 0, 7;
%e 32, 24, 0, 16, 0, 0, 0, 8;
%e 27, 0, 18, 0, 0, 0, 0, 0, 9;
%e 40, 20, 0, 0, 20, 0, 0, 0, 0, 10;
%e 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;
%e 72, 48, 36, 24, 0, 24, 0, 0, 0, 0, 0, 12;
%e 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13;
%e 56, 28, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 14;
%e 60, 0, 30, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15;
%e 80, 64, 0, 48, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 16;
%e ...
%e For n = 6 the partitions of 6 into equal parts are [6], [3, 3], [2, 2, 2], [1, 1, 1, 1, 1, 1]. Then, for k = 2 the sum of the parts that are multiples of 2 is 6 + 2 + 2 + 2 = 12, so T(6,2) = 12.
%Y Column 1 is A038040.
%Y Row sums give A034718.
%Y Leading diagonal gives A000027.
%Y The number of positive terms in row n is A000005(n).
%Y Cf. A126988, A130540, A134577, A244051.
%K nonn,tabl
%O 1,2
%A _Omar E. Pol_, Nov 21 2019
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